You have two denominators: x - 1 and 1 - x2 = (1 - x)(1 + x). With a "minus" sign, the first denominator becomes -(1 - x). Take the "minus" sign through the numerator, and you get a subtraction on top.

Use the method illustrated here and multiply, top and bottom, by (1 - x2). This will immediately simplify the fraction considerably!